Discussion
What is the characteristic impedance of a quarter wave transformer matching 200 ohms to 50 ohms?
Answer: B
The transformer impedance is the geometric mean of the two:
\[ Z = \sqrt{200 \times 50} = 100 \]
so 100 ohms. The arithmetic mean is the natural wrong answer and is worth guarding against. On a typical substrate a hundred ohm line is narrow but perfectly printable, which is part of why the technique is so common. The geometric mean rule applies to any quarter wave transformer, in any medium, and is worth remembering in that general form.
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